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Chapter 26 DC Circuits

Chapter 26 DC Circuits. 26-7 Am-, Volt-, and Ohm-meters. An ammeter measures current; a voltmeter measures voltage. Both are based on galvanometers, unless they are digital. Basic constraint: don’t disturb the circuit you want to measure.

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Chapter 26 DC Circuits

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  1. Chapter 26DC Circuits

  2. 26-7 Am-, Volt-, and Ohm-meters An ammeter measures current; a voltmeter measures voltage. Both are based on galvanometers, unless they are digital. Basic constraint: don’t disturb the circuit you want to measure. Summary: An ammeter must be in series with the current it is to measure; a voltmeter must be in parallel with the voltage it is to measure.

  3. 26-7 Am-, Volt-, and Ohm-meters Ammeter: The current in a circuit passes through the ammeter; the ammeter should have low resistance so as not to affect the current. Example 26-15: Ammeter design. Design an ammeter to read 1.0 A at full scale using a galvanometer with a full-scale sensitivity of 50 μA and a resistance r = 30 Ω. Check if the scale is linear.

  4. 26-7 Am-, Volt-, and Ohm-meters A voltmeter should not affect the voltage across the circuit element it is measuring; therefore its resistance should be very large. Example 26-16: Voltmeter design. Using a galvanometer with internal resistance 30 Ω and full-scale current sensitivity of 50 μA, design a voltmeter that reads from 0 to 15 V. Is the scale linear?

  5. 26-7 Am-, Volt-, and Ohm-meters An ohmmeter measures resistance; it requires a battery to provide a current.

  6. Summary of Chapter 26 • A source of emf transforms energy from some other form to electrical energy. • A battery is a source of emf in parallel with an internal resistance. • Resistors in series:

  7. Summary of Chapter 26 • Resistors in parallel: • Kirchhoff’s rules: • Sum of currents entering a junction equals sum of currents leaving it. • Total potential difference around closed loop is zero.

  8. Summary of Chapter 26 • RC circuit has a characteristic time constant: • To avoid shocks, don’t allow your body to become part of a complete circuit. • Ammeter: measures current. • Voltmeter: measures voltage.

  9. Chapter 27Magnetism

  10. Units of Chapter 27 • Magnets and Magnetic Fields • Electric Currents Produce Magnetic Fields • Force on an Electric Current in a Magnetic Field; Definition of B • Force on an Electric Charge Moving in a Magnetic Field • Torque on a Current Loop; Magnetic Dipole Moment

  11. Units of Chapter 27 • Applications: Motors, Loudspeakers, Galvanometers • Discovery and Properties of the Electron • The Hall Effect • Mass Spectrometer

  12. 27-1 Magnets and Magnetic Fields Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract.

  13. 27-1 Magnets and Magnetic Fields However, if you cut a magnet in half, you don’t get a north pole and a south pole – you get two smaller magnets.

  14. 27-1 Magnets and Magnetic Fields Magnetic fields can be visualized using magnetic field lines, which are always closed loops.

  15. 27-1 Magnets and Magnetic Fields The Earth’s magnetic field is similar to that of a bar magnet. Note that the Earth’s “North Pole” is really a south magnetic pole, as the north ends of magnets are attracted to it.

  16. 27-1 Magnets and Magnetic Fields A uniform magnetic field is constant in magnitude and direction. The field between these two wide poles is nearly uniform.

  17. 27-2 Electric Currents Produce Magnetic Fields Experiment shows that an electric current produces a magnetic field. The direction of the field is given by a right-hand rule.

  18. 27-2 Electric Currents Produce Magnetic Fields Here we see the field due to a current loop; the direction is again given by a right-hand rule.

  19. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B A magnet exerts a force on a current-carrying wire. The direction of the force is given by a right-hand rule.

  20. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation: This equation defines the magnetic field B. In vector notation:

  21. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Unit of B: the tesla, T: 1 T = 1 N/A·m. Another unit sometimes used: the gauss (G): 1 G = 10-4 T or more commonly the kiloGauss 1 kG = 10-1 T.

  22. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-1: Magnetic Force on a current-carrying wire. A wire carrying a 30-A current has a length l = 12 cm between the pole faces of a magnet at an angleθ = 60°, as shown.The magnetic field is approximately uniform at 0.90 T. We ignore the field beyond the pole pieces. What is the magnitude of the force on the wire?

  23. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-2: Measuring a magnetic field. A rectangular loop of wire hangs vertically as shown. A magnetic field B is directed horizontally, perpendicular to the wire, and points out of the page at all points. The magnetic field is very nearly uniform along the horizontal portion of wire ab (length l = 10.0 cm) which is near the center of the gap of a large magnet producing the field. The top portion of the wire loop is free of the field. The loop hangs from a balance which measures a downward magnetic force (in addition to the gravitational force) of F = 3.48 x 10-2 N when the wire carries a current I = 0.245 A. What is the magnitude of the magnetic field B?

  24. 27-3 Force on an Electric Current in a Magnetic Field; Definition of B Example 27-3: Magnetic Force on a semicircular wire. A rigid wire, carrying a current I, consists of a semicircle of radius R and two straight portions as shown. The wire lies in a plane perpendicular to a uniform magnetic field B0. Note choice of x and y axis. The straight portions each have length lwithin the field. Determine the net force on the wire due to the magnetic field B0.

  25. 27-4 Force on an Electric Charge Moving in a Magnetic Field The force on a moving charge is related to the force on a current: Once again, the direction is given by a right-hand rule.

  26. 27-4 Force on an Electric Charge Moving in a Magnetic Field Conceptual Example 27-4: Negative charge near a magnet. A negative charge -Q is placed at rest near a magnet. Will the charge begin to move? Will it feel a force? What if the charge were positive, +Q?

  27. 27-4 Force on an Electric Charge Moving in a Magnetic Field Example 27-5: Magnetic force on a proton. A magnetic field exerts a force of 8.0 x 10-14 N toward the west on a proton moving vertically upward at a speed of 5.0 x 106 m/s (a). When moving horizontally in a northerly direction, the force on the proton is zero (b). Determine the magnitude and direction of the magnetic field in this region. (The charge on a proton is q = +e = 1.6 x 10-19 C.)

  28. 27-4 Force on an Electric Charge Moving in a Magnetic Field If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle.

  29. 27-4 Force on an Electric Charge Moving in a Magnetic Field Example 27-7: Electron’s path in a uniform magnetic field. An electron travels at 2.0 x 107 m/s in a plane perpendicular to a uniform 0.010-T magnetic field. Describe its path quantitatively.

  30. x x x x x x x x x x x x x x x x x x v q ConcepTest 27.1a Magnetic Force I A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? 1) out of the page 2) into the page 3) downward 4) to the right 5) to the left

  31. x x x x x x x x x x x x x x x x x x v q F ConcepTest 27.1a Magnetic Force I A positive charge enters a uniform magnetic field as shown. What is the direction of the magnetic force? 1) out of the page 2) into the page 3) downward 4) to the right 5) to the left Using the right-hand rule, you can see that the magnetic force is directed to the left. Remember that the magnetic force must be perpendicularto BOTH the B field and the velocity.

  32. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 ConcepTest 27.4a Mass Spectrometer I Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge? 3) both charges are equal 4) impossible to tell from the picture

  33. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x 1 2 ConcepTest 27.4a Mass Spectrometer I Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. Which particle has the bigger charge? 3) both charges are equal 4) impossible to tell from the picture The relevant equation for us is: . According to this equation, the bigger the charge, the smaller the radius. Follow-up: What is the sign of the charges in the picture?

  34. 27-4 Force on an Electric Charge Moving in a Magnetic Field • Problem solving: Magnetic fields – things to remember: • The magnetic force is perpendicular to the magnetic field direction. • The right-hand rule is useful for determining directions. • Equations in this chapter give magnitudes only. The right-hand rule gives the direction.

  35. 27-4 Force on an Electric Charge Moving in a Magnetic Field

  36. 27-4 Force on an Electric Charge Moving in a Magnetic Field Conceptual Example 27-9: A helical path. What is the path of a charged particle in a uniform magnetic field if its velocity is not perpendicular to the magnetic field?

  37. 27-4 Force on an Electric Charge Moving in a Magnetic Field The aurora borealis (northern lights) is caused by charged particles from the solar wind spiraling along the Earth’s magnetic field, and colliding with air molecules.

  38. 27-4 Force on an Electric Charge Moving in a Magnetic Field Conceptual Example 27-10: Velocity selector, or filter: crossed E and B fields. Some electronic devices and experiments need a beam of charged particles all moving at nearly the same velocity. This can be achieved using both a uniform electric field and a uniform magnetic field, arranged so they are at right angles to each other. Particles of charge q pass through slit S1 and enter the region where B points into the page and E points down from the positive plate toward the negative plate. If the particles enter with different velocities, show how this device “selects” a particular velocity, and determine what this velocity is.

  39. 27-5 Torque on a Current Loop; Magnetic Dipole Moment The forces on opposite sides of a current loop will be equal and opposite (if the field is uniform and the loop is symmetric), but there may be a torque. The torque is given by

  40. 27-5 Torque on a Current Loop; Magnetic Dipole Moment The quantity NIA is called the magnetic dipole moment, μ: The potential energy of the loop depends on its orientation in the field:

  41. 27-5 Torque on a Current Loop; Magnetic Dipole Moment Example 27-11: Torque on a coil. A circular coil of wire has a diameter of 20.0 cm and contains 10 loops. The current in each loop is 3.00 A, and the coil is placed in a 2.00-T external magnetic field. Determine the maximum and minimum torque exerted on the coil by the field.

  42. Midterm # 1 • # 2 Pencil • 1 sheet 8 ½” X 11” with EQUATIONS you have written on it • Non-graphical calculator, no programs • In your best interests not to be late

  43. Questions?

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